The governor said that he needs to see a "road map" toward the possible ratification of the deal, which was rejected by four of 15 bargaining units, although 57 percent of unionized state workers voted for it.

"I have asked (Ojakian) to converse with them about what is a road map to acceptance or approval of an agreement," Malloy said. "I have to understand how we would get from where we are now with a good agreement that's been rejected, to a clarified agreement that could be accepted."

Malloy described the road map as "how to get from point A to point B." He said that the unions apparently have to "get past" current rules that require 14 of the 15 unions to approve concessions.

On Tuesday, SEBAC reached out to Malloy, asking for renewed concessions' talks.

Matt O'Connor, spokesman for SEBAC, said Thursday that union leaders, who have been attempting to stave off Malloy's planned program cuts and as many as 6,600 layoffs, have been meeting all week to see how the rejected deal can win new life.

The state Senate last week approved a bill aimed at capping so-called longevity payments to veteran state workers and ending the use of overtime to calculate pensions for retirees. But the pro-union House of Representatives has shelved the bill. Related legislation gives SEBAC until the end of August to somehow skirt its bylaws and adopt the concessions.

"Our view remains that we should get back to discussions as soon as possible," O'Connor said in a statement. "That being said, we are glad to see there is mutual interest in both sides in finalizing an agreement. And leaders are confident that we can because so much is on the line -- from job cuts to service reductions to contracting-out. They know that the status quo is not an option and that Connecticut needs a path forward."